Question: Simplify to lowest terms. $\dfrac{48}{72}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 48 and 72? $48 = 2\cdot2\cdot2\cdot2\cdot3$ $72 = 2\cdot2\cdot2\cdot3\cdot3$ $\mbox{GCD}(48, 72) = 2\cdot2\cdot2\cdot3 = 24$ $\dfrac{48}{72} = \dfrac{2 \cdot 24}{ 3\cdot 24}$ $\hphantom{\dfrac{48}{72}} = \dfrac{2}{3} \cdot \dfrac{24}{24}$ $\hphantom{\dfrac{48}{72}} = \dfrac{2}{3} \cdot 1$ $\hphantom{\dfrac{48}{72}} = \dfrac{2}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{48}{72}= \dfrac{2\cdot24}{2\cdot36}= \dfrac{2\cdot 2\cdot12}{2\cdot 2\cdot18}= \dfrac{2\cdot 2\cdot 2\cdot6}{2\cdot 2\cdot 2\cdot9}= \dfrac{2\cdot 2\cdot 2\cdot 3\cdot2}{2\cdot 2\cdot 2\cdot 3\cdot3}= \dfrac{2}{3}$